The exact density functional for the ground-state energy is strictly self-interaction-free (i.e., orbitals demonstrably do not self-interact), but many approximations to it, including the local-spin-density (LSD) approximation for exchange and correlation, are not. We present two related methods for the self-interaction correction (SIC) of any density functional for the energy; correction of the self-consistent one-electron potenial follows naturally from the variational principle. Both methods are sanctioned by the Hohenberg-Kohn theorem. Although the first method introduces an orbital-dependent single-particle potential, the second involves a local potential as in the Kohn-Sham scheme. We apply the first method to LSD and show that it properly conserves the number content of the exchange-correlation hole, while substantially improving the description of its shape. We apply this method to a number of physical problems, where the uncorrected LSD approach produces systematic errors. We find systematic improvements, qualitative as well as quantitative, from this simple correction. Benefits of SIC in atomic calculations include (i) improved values for the total energy and for the separate exchange and correlation pieces of it, (ii) accurate binding energies of negative ions, which are wrongly unstable in LSD, (iii) more accurate electron densities, (iv) orbital eigenvalues that closely approximate physical removal energies, including relaxation, and (v) correct longrange behavior of the potential and density. It appears that SIC can also remedy the LSD underestimate of the band gaps in insulators (as shown by numerical calculations for the rare-gas solids and CuCl), and the LSD overestimate of the cohesive energies of transition metals. The LSD spin splitting in atomic Ni and $s\ensuremath{-}d$ interconfigurational energies of transition elements are almost unchanged by SIC. We also discuss the admissibility of fractional occupation numbers, and present a parametrization of the electron-gas correlation energy at any density, based on the recent results of Ceperley and Alder.

Self-interaction correction to density-functional approximations for many-electron systems

I. Introduction: Conceptual vs Fundamental andComputational Aspects of DFT1793II. Fundamental and Computational Aspects of DFT 1795A. The Basics of DFT: The Hohenberg−KohnTheorems1795B. DFT as a Tool for Calculating Atomic andMolecular Properties: The Kohn−ShamEquations1796C. Electronic Chemical Potential andElectronegativity: Bridging Computational andConceptual DFT1797III. DFT-Based Concepts and Principles 1798A. General Scheme: Nalewajski’s ChargeSensitivity Analysis1798B. Concepts and Their Calculation 18001. Electronegativity and the ElectronicChemical Potential18002. Global Hardness and Softness 18023. The Electronic Fukui Function, LocalSoftness, and Softness Kernel18074. Local Hardness and Hardness Kernel 18135. The Molecular Shape FunctionsSimilarity 18146. The Nuclear Fukui Function and ItsDerivatives18167. Spin-Polarized Generalizations 18198. Solvent Effects 18209. Time Evolution of Reactivity Indices 1821C. Principles 18221. Sanderson’s Electronegativity EqualizationPrinciple18222. Pearson’s Hard and Soft Acids andBases Principle18253. The Maximum Hardness Principle 1829IV. Applications 1833A. Atoms and Functional Groups 1833B. Molecular Properties 18381. Dipole Moment, Hardness, Softness, andRelated Properties18382. Conformation 18403. Aromaticity 1840C. Reactivity 18421. Introduction 18422. Comparison of Intramolecular ReactivitySequences18443. Comparison of Intermolecular ReactivitySequences18494. Excited States 1857D. Clusters and Catalysis 1858V. Conclusions 1860VI. Glossary of Most Important Symbols andAcronyms1860VII. Acknowledgments 1861VIII. Note Added in Proof 1862IX. References 1865

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Conceptual density functional theory.

In order to discriminate between approximations to the exchange-correlation energy EXC[ρ↑,ρ↓], we employ the criterion of whether the functional is fitted to a certain experimental data set or if it is constructed to satisfy physical constraints. We present extensive test calculations for atoms and molecules, with the nonempirical local spin-density (LSD) and the Perdew–Burke–Ernzerhof (PBE) functional and compare our results with results obtained with more empirical functionals. For the atomization energies of the G2 set, we find that the PBE functional shows systematic errors larger than those of commonly used empirical functionals. The PBE ionization potentials, electron affinities, and bond lengths are of accuracy similar to those obtained from empirical functionals. Furthermore, a recently proposed hybrid scheme using exact exchange together with PBE exchange and correlation is investigated. For all properties studied here, the PBE hybrid gives an accuracy comparable to the frequently used empirical ...

Assessment of the Perdew–Burke–Ernzerhof exchange-correlation functional

A scheme that reduces the calculations of ground-state properties of systems of interacting particles exactly to the solution of single-particle Hartree-type equations has obvious advantages. It is not surprising, then, that the density functional formalism, which provides a way of doing this, has received much attention in the past two decades. The quality of the energy surfaces calculated using a simple local-density approximation for exchange and correlation exceeds by far the original expectations. In this work, the authors survey the formalism and some of its applications (in particular to atoms and small molecules) and discuss the reasons for the successes and failures of the local-density approximation and some of its modifications.

The density functional formalism, its applications and prospects

Preface Acknowledgements Notation Part I. Overview and Background Topics: 1. Introduction 2. Overview 3. Theoretical background 4. Periodic solids and electron bands 5. Uniform electron gas and simple metals Part II. Density Functional Theory: 6. Density functional theory: foundations 7. The Kohn-Sham ansatz 8. Functionals for exchange and correlation 9. Solving the Kohn-Sham equations Part III. Important Preliminaries on Atoms: 10. Electronic structure of atoms 11. Pseudopotentials Part IV. Determination of Electronic Structure, The Three Basic Methods: 12. Plane waves and grids: basics 13. Plane waves and grids: full calculations 14. Localized orbitals: tight binding 15. Localized orbitals: full calculations 16. Augmented functions: APW, KKR, MTO 17. Augmented functions: linear methods Part V. Predicting Properties of Matter from Electronic Structure - Recent Developments: 18. Quantum molecular dynamics (QMD) 19. Response functions: photons, magnons ... 20. Excitation spectra and optical properties 21. Wannier functions 22. Polarization, localization and Berry's phases 23. Locality and linear scaling O (N) methods 24. Where to find more Appendixes References Index.

Electronic Structure: Basic Theory and Practical Methods

We have derived the general solution of a wave equation describing the dynamics of two-layer viscoelastic polymer materials of arbitrary thickness deposited on solid (quartz) surfaces in a fluid environment. Within the Voight model of viscoelastic element, we calculate the acoustic response of the system to an applied shear stress, i.e. we find the shift of the quartz generator resonance frequency and of the dissipation factor, and show that it strongly depends on the viscous loading of the adsorbed layers and on the shear storage and loss moduli of the overlayers. These results can readily be applied to quartz crystal acoustical measurements of the viscoelasticity of polymers which conserve their shape under the shear deformations and do not flow, and layered structures such as protein films adsorbed from solution onto the surface of self-assembled monolayers.

https://iopscience.iop.org/article/10.1238/Physica.Regular.059a00391/pdf

Viscoelastic Acoustic Response of Layered Polymer Films at Fluid-Solid Interfaces: Continuum Mechanics Approach

The Mott formula for the thermopower, $S=\frac{(\frac{{\ensuremath{\pi}}^{2}}{3})(\frac{{k}_{B}^{2}T}{e}){\ensuremath{\sigma}}^{\ensuremath{'}}}{\ensuremath{\sigma}}$, and the Wiedemann-Franz law, $\frac{K}{\ensuremath{\sigma}T}={(\frac{{k}_{B}}{e})}^{2}(\frac{{\ensuremath{\pi}}^{2}}{3})$, are shown to be exact for independent electrons interacting with static impurities and phonons treated in the adiabatic approximation. This is true irrespective of the interaction strength. These results are derived using a Green's-function technique that emphasizes the importance of corrections to the free-electron heat current operator. These corrections have frequently been neglected in the past. The Green's-function technique is well suited for going beyond the adiabatic phonon approximation, and the implications of doing so are briefly discussed.

Mott's formula for the thermopower and the Wiedemann-Franz law

Starting from a formula relating the exchange-correlation (XC) energy of the Kohn-Sham density-functional formalism to the XC hole, we discuss some general but approximate descriptions of XC effects in inhomogeneous electron systems, in particular valence electrons, using homogeneous-electron-gas data as input. The new descriptions have all the virtues of the local-density (LD) approximation, including the computational simplicity of a local XC potential, and it reduces to the latter in the proper limit. In addition, they have a physically motivated nonlocal dependence on the electron density, which results in such desirable features as an asymptotical ${r}^{\ensuremath{-}1}$ behavior far away from, e.g., atoms and a ${z}^{\ensuremath{-}1}$ behavior of the potential outside solid surfaces. We present two explicit forms of the XC energy functional, one which is exact for a system with almost constant density but with possibly spatially rapid variations, and another which is exact in some simple limits. Illustrations on atoms show them to reduce the error in the total energy by about one order of magnitude compared with the LD approximation. Applications to surfaces show a reasonable modeling of the image-potential effect but also illustrate shortcomings of the approximations. We also point out shortcomings of two earlier methods to extend the LD approximation, the gradient expansion, and the expansion to second order in the density variations, when they are applied to inhomogeneous systems.

Descriptions of exchange and correlation effects in inhomogeneous electron systems

Missing mass effect in biosensor's QCM applications.

Room-temperature Coulomb blockade of charge transport through composite nanostructures containing organic interlinks has recently been observed. A pronounced charging effect in combination with the softness of the molecular links implies that charge transfer gives rise to a significant deformation of these structures. For a simple model system, we show that self-excitation of periodic cluster oscillations in conjunction with sequential processes of cluster charging and decharging appears for a sufficiently large bias voltage. This new ``electron shuttle'' mechanism of discrete charge transfer gives rise to a current through the nanostructure which is proportional to the cluster vibration frequency.

https://arxiv.org/pdf/cond-mat/9711196.pdf

Mats Jonson

Papers

Viscoelastic Acoustic Response of Layered Polymer Films at Fluid-Solid Interfaces: Continuum Mechanics Approach

Mott's formula for the thermopower and the Wiedemann-Franz law

Descriptions of exchange and correlation effects in inhomogeneous electron systems

Missing mass effect in biosensor's QCM applications.

Shuttle Mechanism for Charge Transfer in Coulomb Blockade Nanostructures